Existence, uniqueness, and blow-up analysis of a quasi-linear bi-hyperbolic equation with dynamic boundary conditions-Reference-Cited by-同舟云学术

Existence, uniqueness, and blow-up analysis of a quasi-linear bi-hyperbolic equation with dynamic boundary conditions

Published:2024 Issue:5 Volume:32 Page:3363-3376
ISSN:2688-1594
Container-title:Electronic Research Archive
language:
Short-container-title:era

Author:

Desova Begüm Çalışkan¹,Polat Mustafa²

Affiliation:

1. Department of Information Security Technology, Yeditepe University, Atasehir 34755, Turkey

2. Department of Mathematics, Yeditepe University, Atasehir 34755, Turkey

Abstract

<abstract><p>For this study, we investigate the existence and uniqueness of local solutions and derive a blow-up solution for a quasi-linear bi-hyperbolic equation under dynamic boundary conditions. We utilize the contraction mapping concept to demonstrate the solution's local well-posedness and employ a concavity approach to establish the blow-up result.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Reference13 articles.

1. C. F. Vasconcellos, L. M. Teixeira, Existence, uniqueness and stabilization for a nonlinear plate system with nonlinear damping, Ann. Fac. Sci. Toulouse, 8 (1999), 173–193. https://doi.org/10.5802/afst.928

2. M. Guedda, H. Labani, Nonexistence of global solutions to a class of nonlinear wave equations with dynamic boundary conditions, Bull. Belg. Math. Soc. Simon Stevin, 9 (2002), 39–46.

3. S. T. Wu, L. Y. Tsai, Existence and nonexistence of global solutions for a nonlinear wave equation, Taiwanese J. Math., 13 (2009), 2069–2091. https://doi.org/10.11650/twjm/1500405658

4. V. Georgiev, G. Todorova, Existence of a solution of the wave equation with nonlinear damping and source terms, J. Differ. Equations, 109 (1994), 295–308. https://doi.org/10.1006/jdeq.1994.1051

5. E. Vitillaro, On the wave equation with hyperbolic dynamical boundary conditions, interior and boundary damping and supercritical sources, J. Differ. Equations, 265 (2017), 4873–4941. https://doi.org/10.1016/j.jde.2018.06.022